Chauncey Coventry - where to go for death, 1890?

Chauncey Coventry - where to go for death, 1890?

Chauncey Coventry died in Sullivan County in 1890. I understand that the state should have been keeping some records by this point. What is the best place to try to get the official death information? I know I can go to the state site, with a long wait - is there another place I can go to get the official death record?